In a school meeting, 1/3 of people present are parents, 2/7 of people present are teachers, the remainder are pupils. Find the fraction of pupils present. If there are 64 pupils present, how many people are in the meeting? How many parents present?

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Asked on June 26, 2026Mathematics

This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.

Accepted Answer · 2026-06-26T18:16:02.652Z

here are the solutions to the questions from the image. Question 48: Father is 25 years older than his daughter. In 5 years' time, the father will be twice as old as the daughter. a) How old is the daughter? b) How old is the father? c) How old will be the daughter? d) How old will be the father? Step 1: Set up equations for current ages. Let D be the daughter's current age and F be the father's current age. From the first statement: F = D + 25 (Equation 1) Step 2: Set up equations for ages in 5 years. In 5 years, daughter's age will be D+5. In 5 years, father's age will be F+5. From the second statement: F+5 = 2(D+5) (Equation 2) Step 3: Solve the system of equations. Substitute Equation 1 into Equation 2: (D+25) + 5 = 2(D+5) D + 30 = 2D + 10 30 - 10 = 2D - D D = 20 Now find F using Equation 1: F = 20 + 25 = 45 Step 4: Calculate ages in 5 years. Daughter's age in 5 years = D+5 = 20+5 = 25. Father's age in 5 years = F+5 = 45+5 = 50. a) How old is the daughter? The daughter is 20 years old. b) How old is the father? The father is 45 years old. c) How old will be the daughter? In 5 years, the daughter will be 25 years old. d) How old will be the father? In 5 years, the father will be 50 years old. Question 49: Find the missing numbers in the sequences a) 1, 4, 7, 10, ____, ____ b) 17, 19, 23, 29, ____, ____ c) 2, 3, 5, ____, ____ a) 1, 4, 7, 10, ____, ____ Step 1: Identify the pattern. This is an arithmetic sequence where each term is obtained by adding 3 to the previous term (4-1=3, 7-4=3, 10-7=3). Step 2: Find the missing numbers. The next number is 10+3=13. The number after that is 13+3=16. The missing numbers are 13, 16. b) 17, 19, 23, 29, ____, ____ Step 1: Identify the pattern. The differences between consecutive terms are: 19-17=2 23-19=4 29-23=6 The differences are increasing by 2 each time (2, 4, 6). Step 2: Find the missing numbers. The next difference should be 6+2=8. So, 29+8=37. The next difference should be 8+2=10. So, 37+10=47. The missing numbers are 37, 47. c) 2, 3, 5, ____, ____ Step 1: Identify the pattern. This sequence consists of prime numbers in ascending order. Step 2: Find the missing numbers. The prime numbers after 5 are 7 and 11. The missing numbers are 7, 11. Question 50: The cost price of a cow is 75000 Frw and the selling price is 90000 Frw. Calculate the percentage profit. Step 1: Calculate the profit. Profit = Selling Price - Cost Price Profit = 90000 Frw - 75000 Frw = 15000 Frw Step 2: Calculate the percentage profit. Percentage Profit = ProfitCost Price × 100\% Percentage Profit = 15000 Frw75000 Frw × 100\% Percentage Profit = (1)/(5) × 100\% = 20\% The percentage profit is 20\%. Question 51: The sum of three consecutive even numbers is 78. Find the numbers. Step 1: Represent the consecutive even numbers. Let the first even number be x. The second consecutive even number is x+2. The third consecutive even number is x+4. Step 2: Set up an equation and solve for x. x + (x+2) + (x+4) = 78 3x + 6 = 78 3x = 78 - 6 3x = 72 x = (72)/(3) = 24 Step 3: Find the three numbers. The first number is x = 24. The second number is x+2 = 24+2 = 26. The third number is x+4 = 24+4 = 28. The three consecutive even numbers are 24, 26, 28. Question 52: A family eats 6 kg of rice for 15 days. How many kg of rice does the family eat in 6 days? Step 1: Calculate the daily consumption rate. Daily consumption = 6 kg15 days = (2)/(5) kg/day Step 2: Calculate the amount of rice eaten in 6 days. Rice in 6 days = Daily consumption × 6 days Rice in 6 days = (2)/(5) kg/day × 6 days = (12)/(5) kg Rice in 6 days = 2.4 kg The family eats 2.4 kg of rice in 6 days. Question 53: Express 20 cm as a fraction of 2 m and simplify your answer. Step 1: Convert units to be consistent. Since 1 m = 100 cm, then 2 m = 2 × 100 cm = 200 cm. Step 2: Form the fraction and simplify. Fraction = 20 cm200 cm = (20)/(200) = (1)/(10) The fraction is (1)/(10). Question 54: On a map, 5 dm represents 2 km. Calculate the scale of the map. Step 1: Convert both measurements to the same unit, e.g., centimeters. 1 dm = 10 cm, so 5 dm = 5 × 10 cm = 50 cm. 1 km = 1000 m = 1000 × 100 cm = 100000 cm. So, 2 km = 2 × 100000 cm = 200000 cm. Step 2: Express the scale as a ratio and simplify to 1:N. Scale = Map distanceActual distance = 50 cm200000 cm Scale = (50)/(200000) = (1)/(4000) The scale of the map is 1:4000. Question 55: James, Robert and Amos shared some money in the ratio of 4:3:9 respectively. If Amos got 3000 Frw more than Robert. a) How much money did Amos get? b) How much money did James get? c) How much money did Robert get? d) How much money was shared? Step 1: Represent the shares using a common multiplier. Let the common multiplier be x. James's share = 4x Robert's share = 3x Amos's share = 9x Step 2: Use the given information to find x. Amos got 3000 Frw more than Robert: 9x - 3x = 3000 Frw 6x = 3000 Frw x = (3000)/(6) = 500 Frw Step 3: Calculate each person's share. a) How much money did Amos get? Amos's share = 9x = 9 × 500 Frw = 4500 Frw. Amos got 4500 Frw. b) How much money did James get? James's share = 4x = 4 × 500 Frw = 2000 Frw. James got 2000 Frw. c) How much money did Robert get? Robert's share = 3x = 3 × 500 Frw = 1500 Frw. Robert got 1500 Frw. d) How much money was shared? Total money shared = James's share + Robert's share + Amos's share Total money = 2000 Frw + 1500 Frw + 4500 Frw = 8000 Frw Alternatively, total parts = 4+3+9 = 16. Total money = 16x = 16 × 500 Frw = 8000 Frw. The total money shared was 8000 Frw. Question 56: Find the value of angles marked with letters X and Y. Step 1: Identify the angles in the triangle. The interior angles of the triangle are 60^, Y, and 70^. Step 2: Calculate angle Y using the sum of angles in a triangle. The sum of angles in a triangle is 180^. 60^ + Y + 70^ = 180^ 130^ + Y = 180^ Y = 180^ - 130^ = 50^ Step 3: Calculate angle X. Angle X and the 60^ angle form a linear pair (angles on a straight line), so their sum is 180^. X + 60^ = 180^ X = 180^ - 60^ = 120^ The values of the angles are X = 120^, Y = 50^. Question 57: Work out and simplify completely a) (1)/(2) + (1)/(3) + (1)/(5) b) ((1)/(4) + (1)/(2)) ÷ (3)/(4) c) (3 - (1)/(3)) × 13 a) (1)/(2) + (1)/(3) + (1)/(5) Step 1: Find a common denominator for 2, 3, and 5, which is 30. (1)/(2) + (1)/(3) + (1)/(5) = (1 × 15)/(2 × 15) + (1 × 10)/(3 × 10) + (1 × 6)/(5 × 6) = (15)/(30) + (10)/(30) + (6)/(30) Step 2: Add the fractions. = (15+10+6)/(30) = (31)/(30) The simplified answer is (31)/(30). b) ((1)/(4) + (1)/(2)) ÷ (3)/(4) Step 1: Add the fractions in the parenthesis. (1)/(4) + (1)/(2) = (1)/(4) + (2)/(4) = (1+2)/(4) = (3)/(4) Step 2: Perform the division. (3)/(4) ÷ (3)/(4) = (3)/(4) × (4)/(3) = 1 The simplified answer is 1. c) (3 - (1)/(3)) × 13 Step 1: Subtract the fractions in the parenthesis. 3 - (1)/(3) = (9)/(3) - (1)/(3) = (9-1)/(3) = (8)/(3) Step 2: Multiply the result by 13. (8)/(3) × 13 = (8 × 13)/(3) = (104)/(3) The simplified answer is (104)/(3). Question 58: Write the following fractions in figures a) Three tenths b) Eleven and a quarter c) Twelve thirty first a) Three tenths (3)/(10) b) Eleven and a quarter 11(1)/(4) or (45)/(4) c) Twelve thirty first (12)/(31) Question 59: Simplify completely (x^2 - 1)/(x^2 + x) Step 1: Factorize the numerator using the difference of squares formula (a^2 - b^2 = (a-b)(a+b)). x^2 - 1 = (x-1)(x+1) Step 2: Factorize the denominator by taking out the common factor x. x^2 + x = x(x+1) Step 3: Substitute the factored expressions back into the fraction and simplify. ((x-1)(x+1))/(x(x+1)) Cancel out the common factor (x+1), assuming x ≠ -1. (x-1)/(x) The simplified expression is (x-1)/(x). Question 60: If (2)/(5) of the pupils in P6 class are girls. Find the number of boys in the class if there are 120 pupils. Step 1: Find the fraction of boys in the class. The total fraction of pupils is 1. Fraction of boys = 1 - Fraction of girls Fraction of boys = 1 - (2)/(5) = (5)/(5) - (2)/(5) = (3)/(5) Step 2: Calculate the number of boys. Number of boys = Fraction of boys × Total pupils Number of boys = (3)/(5) × 120 Number of boys = 3 × (120)/(5) = 3 × 24 = 72 There are 72 boys in the class. Question 61: Senega, Kallas and Khadija contributed money to start a company. Senega paid (1)/(2) of the cost and Kallas paid (1)/(4) of the cost. a) What fraction did Khadija contribute? b) If Khadija contributed 200000 Frw, what was the total cost? a) What fraction did Khadija contribute? Step 1: Find the combined fraction contributed by Senega and Kallas. Senega's fraction + Kallas's fraction = (1)/(2) + (1)/(4) = (2)/(4) + (1)/(4) = (3)/(4) Step 2: Find Khadija's fraction. The total fraction of the cost is 1. Khadija's fraction = 1 - (3)/(4) = (4)/(4) - (3)/(4) = (1)/(4) Khadija contributed (1)/(4) of the cost. b) If Khadija contributed 200000 Frw, what was the total cost? Step 1: Use Khadija's contribution and fraction to find the total cost. Let the total cost be C. Khadija's fraction × C = Khadija's contribution (1)/(4) × C = 200000 Frw Step 2: Solve for C. C = 200000 Frw × 4 C = 800000 Frw The total cost was 800000 Frw. Question 62: Observe the following cylinder. The image shows a cylinder with height 20 cm and radius 7 cm. a) Calculate the total surface area of this cylinder. Step 1: Identify the given dimensions and the formula for the total surface area of a cylinder. Height h = 20 cm Radius r = 7 cm The formula for the total surface area (TSA) of a cylinder is TSA = 2 r^2 + 2 rh. Use = (22)/(7). Step 2: Substitute the values into the formula and calculate. TSA = 2 × (22)/(7) × (7 cm)^2 + 2 × (22)/(7) × 7 cm × 20 cm TSA = 2 × (22)/(7) × 49 cm^2 + 2 × 22 × 20 cm^2 TSA = 2 × 22 × 7 cm^2 + 880 cm^2 TSA = 308 cm^2 + 880 cm^2 TSA = 1188 cm^2 The total surface area of the cylinder is 1188 cm^2. You've tackled a lot of questions! What's next? 📸

Accepted Answer · 2026-06-26T18:16:02.652Z

here are the solutions to the questions from the image. Question 48: Father is 25 years older than his daughter. In 5 years' time, the father will be twice as old as the daughter. a) How old is the daughter? b) How old is the father? c) How old will be the daughter? d) How old will be the father? Step 1: Set up equations for current ages. Let D be the daughter's current age and F be the father's current age. From the first statement: F = D + 25 (Equation 1) Step 2: Set up equations for ages in 5 years. In 5 years, daughter's age will be D+5. In 5 years, father's age will be F+5. From the second statement: F+5 = 2(D+5) (Equation 2) Step 3: Solve the system of equations. Substitute Equation 1 into Equation 2: (D+25) + 5 = 2(D+5) D + 30 = 2D + 10 30 - 10 = 2D - D D = 20 Now find F using Equation 1: F = 20 + 25 = 45 Step 4: Calculate ages in 5 years. Daughter's age in 5 years = D+5 = 20+5 = 25. Father's age in 5 years = F+5 = 45+5 = 50. a) How old is the daughter? The daughter is 20 years old. b) How old is the father? The father is 45 years old. c) How old will be the daughter? In 5 years, the daughter will be 25 years old. d) How old will be the father? In 5 years, the father will be 50 years old. Question 49: Find the missing numbers in the sequences a) 1, 4, 7, 10, ____, ____ b) 17, 19, 23, 29, ____, ____ c) 2, 3, 5, ____, ____ a) 1, 4, 7, 10, ____, ____ Step 1: Identify the pattern. This is an arithmetic sequence where each term is obtained by adding 3 to the previous term (4-1=3, 7-4=3, 10-7=3). Step 2: Find the missing numbers. The next number is 10+3=13. The number after that is 13+3=16. The missing numbers are 13, 16. b) 17, 19, 23, 29, ____, ____ Step 1: Identify the pattern. The differences between consecutive terms are: 19-17=2 23-19=4 29-23=6 The differences are increasing by 2 each time (2, 4, 6). Step 2: Find the missing numbers. The next difference should be 6+2=8. So, 29+8=37. The next difference should be 8+2=10. So, 37+10=47. The missing numbers are 37, 47. c) 2, 3, 5, ____, ____ Step 1: Identify the pattern. This sequence consists of prime numbers in ascending order. Step 2: Find the missing numbers. The prime numbers after 5 are 7 and 11. The missing numbers are 7, 11. Question 50: The cost price of a cow is 75000 Frw and the selling price is 90000 Frw. Calculate the percentage profit. Step 1: Calculate the profit. Profit = Selling Price - Cost Price Profit = 90000 Frw - 75000 Frw = 15000 Frw Step 2: Calculate the percentage profit. Percentage Profit = ProfitCost Price × 100\% Percentage Profit = 15000 Frw75000 Frw × 100\% Percentage Profit = (1)/(5) × 100\% = 20\% The percentage profit is 20\%. Question 51: The sum of three consecutive even numbers is 78. Find the numbers. Step 1: Represent the consecutive even numbers. Let the first even number be x. The second consecutive even number is x+2. The third consecutive even number is x+4. Step 2: Set up an equation and solve for x. x + (x+2) + (x+4) = 78 3x + 6 = 78 3x = 78 - 6 3x = 72 x = (72)/(3) = 24 Step 3: Find the three numbers. The first number is x = 24. The second number is x+2 = 24+2 = 26. The third number is x+4 = 24+4 = 28. The three consecutive even numbers are 24, 26, 28. Question 52: A family eats 6 kg of rice for 15 days. How many kg of rice does the family eat in 6 days? Step 1: Calculate the daily consumption rate. Daily consumption = 6 kg15 days = (2)/(5) kg/day Step 2: Calculate the amount of rice eaten in 6 days. Rice in 6 days = Daily consumption × 6 days Rice in 6 days = (2)/(5) kg/day × 6 days = (12)/(5) kg Rice in 6 days = 2.4 kg The family eats 2.4 kg of rice in 6 days. Question 53: Express 20 cm as a fraction of 2 m and simplify your answer. Step 1: Convert units to be consistent. Since 1 m = 100 cm, then 2 m = 2 × 100 cm = 200 cm. Step 2: Form the fraction and simplify. Fraction = 20 cm200 cm = (20)/(200) = (1)/(10) The fraction is (1)/(10). Question 54: On a map, 5 dm represents 2 km. Calculate the scale of the map. Step 1: Convert both measurements to the same unit, e.g., centimeters. 1 dm = 10 cm, so 5 dm = 5 × 10 cm = 50 cm. 1 km = 1000 m = 1000 × 100 cm = 100000 cm. So, 2 km = 2 × 100000 cm = 200000 cm. Step 2: Express the scale as a ratio and simplify to 1:N. Scale = Map distanceActual distance = 50 cm200000 cm Scale = (50)/(200000) = (1)/(4000) The scale of the map is 1:4000. Question 55: James, Robert and Amos shared some money in the ratio of 4:3:9 respectively. If Amos got 3000 Frw more than Robert. a) How much money did Amos get? b) How much money did James get? c) How much money did Robert get? d) How much money was shared? Step 1: Represent the shares using a common multiplier. Let the common multiplier be x. James's share = 4x Robert's share = 3x Amos's share = 9x Step 2: Use the given information to find x. Amos got 3000 Frw more than Robert: 9x - 3x = 3000 Frw 6x = 3000 Frw x = (3000)/(6) = 500 Frw Step 3: Calculate each person's share. a) How much money did Amos get? Amos's share = 9x = 9 × 500 Frw = 4500 Frw. Amos got 4500 Frw. b) How much money did James get? James's share = 4x = 4 × 500 Frw = 2000 Frw. James got 2000 Frw. c) How much money did Robert get? Robert's share = 3x = 3 × 500 Frw = 1500 Frw. Robert got 1500 Frw. d) How much money was shared? Total money shared = James's share + Robert's share + Amos's share Total money = 2000 Frw + 1500 Frw + 4500 Frw = 8000 Frw Alternatively, total parts = 4+3+9 = 16. Total money = 16x = 16 × 500 Frw = 8000 Frw. The total money shared was 8000 Frw. Question 56: Find the value of angles marked with letters X and Y. Step 1: Identify the angles in the triangle. The interior angles of the triangle are 60^, Y, and 70^. Step 2: Calculate angle Y using the sum of angles in a triangle. The sum of angles in a triangle is 180^. 60^ + Y + 70^ = 180^ 130^ + Y = 180^ Y = 180^ - 130^ = 50^ Step 3: Calculate angle X. Angle X and the 60^ angle form a linear pair (angles on a straight line), so their sum is 180^. X + 60^ = 180^ X = 180^ - 60^ = 120^ The values of the angles are X = 120^, Y = 50^. Question 57: Work out and simplify completely a) (1)/(2) + (1)/(3) + (1)/(5) b) ((1)/(4) + (1)/(2)) ÷ (3)/(4) c) (3 - (1)/(3)) × 13 a) (1)/(2) + (1)/(3) + (1)/(5) Step 1: Find a common denominator for 2, 3, and 5, which is 30. (1)/(2) + (1)/(3) + (1)/(5) = (1 × 15)/(2 × 15) + (1 × 10)/(3 × 10) + (1 × 6)/(5 × 6) = (15)/(30) + (10)/(30) + (6)/(30) Step 2: Add the fractions. = (15+10+6)/(30) = (31)/(30) The simplified answer is (31)/(30). b) ((1)/(4) + (1)/(2)) ÷ (3)/(4) Step 1: Add the fractions in the parenthesis. (1)/(4) + (1)/(2) = (1)/(4) + (2)/(4) = (1+2)/(4) = (3)/(4) Step 2: Perform the division. (3)/(4) ÷ (3)/(4) = (3)/(4) × (4)/(3) = 1 The simplified answer is 1. c) (3 - (1)/(3)) × 13 Step 1: Subtract the fractions in the parenthesis. 3 - (1)/(3) = (9)/(3) - (1)/(3) = (9-1)/(3) = (8)/(3) Step 2: Multiply the result by 13. (8)/(3) × 13 = (8 × 13)/(3) = (104)/(3) The simplified answer is (104)/(3). Question 58: Write the following fractions in figures a) Three tenths b) Eleven and a quarter c) Twelve thirty first a) Three tenths (3)/(10) b) Eleven and a quarter 11(1)/(4) or (45)/(4) c) Twelve thirty first (12)/(31) Question 59: Simplify completely (x^2 - 1)/(x^2 + x) Step 1: Factorize the numerator using the difference of squares formula (a^2 - b^2 = (a-b)(a+b)). x^2 - 1 = (x-1)(x+1) Step 2: Factorize the denominator by taking out the common factor x. x^2 + x = x(x+1) Step 3: Substitute the factored expressions back into the fraction and simplify. ((x-1)(x+1))/(x(x+1)) Cancel out the common factor (x+1), assuming x ≠ -1. (x-1)/(x) The simplified expression is (x-1)/(x). Question 60: If (2)/(5) of the pupils in P6 class are girls. Find the number of boys in the class if there are 120 pupils. Step 1: Find the fraction of boys in the class. The total fraction of pupils is 1. Fraction of boys = 1 - Fraction of girls Fraction of boys = 1 - (2)/(5) = (5)/(5) - (2)/(5) = (3)/(5) Step 2: Calculate the number of boys. Number of boys = Fraction of boys × Total pupils Number of boys = (3)/(5) × 120 Number of boys = 3 × (120)/(5) = 3 × 24 = 72 There are 72 boys in the class. Question 61: Senega, Kallas and Khadija contributed money to start a company. Senega paid (1)/(2) of the cost and Kallas paid (1)/(4) of the cost. a) What fraction did Khadija contribute? b) If Khadija contributed 200000 Frw, what was the total cost? a) What fraction did Khadija contribute? Step 1: Find the combined fraction contributed by Senega and Kallas. Senega's fraction + Kallas's fraction = (1)/(2) + (1)/(4) = (2)/(4) + (1)/(4) = (3)/(4) Step 2: Find Khadija's fraction. The total fraction of the cost is 1. Khadija's fraction = 1 - (3)/(4) = (4)/(4) - (3)/(4) = (1)/(4) Khadija contributed (1)/(4) of the cost. b) If Khadija contributed 200000 Frw, what was the total cost? Step 1: Use Khadija's contribution and fraction to find the total cost. Let the total cost be C. Khadija's fraction × C = Khadija's contribution (1)/(4) × C = 200000 Frw Step 2: Solve for C. C = 200000 Frw × 4 C = 800000 Frw The total cost was 800000 Frw. Question 62: Observe the following cylinder. The image shows a cylinder with height 20 cm and radius 7 cm. a) Calculate the total surface area of this cylinder. Step 1: Identify the given dimensions and the formula for the total surface area of a cylinder. Height h = 20 cm Radius r = 7 cm The formula for the total surface area (TSA) of a cylinder is TSA = 2 r^2 + 2 rh. Use = (22)/(7). Step 2: Substitute the values into the formula and calculate. TSA = 2 × (22)/(7) × (7 cm)^2 + 2 × (22)/(7) × 7 cm × 20 cm TSA = 2 × (22)/(7) × 49 cm^2 + 2 × 22 × 20 cm^2 TSA = 2 × 22 × 7 cm^2 + 880 cm^2 TSA = 308 cm^2 + 880 cm^2 TSA = 1188 cm^2 The total surface area of the cylinder is 1188 cm^2. You've tackled a lot of questions! What's next? 📸

In a school meeting, 1/3 of people present are parents, 2/7 of people present are teachers, the remainder are pupils. Find the fraction of pupils present. If there are 64 pupils present, how many people are in the meeting? How many parents present?

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In a school meeting, 1/3 of people present are parents, 2/7 of people present are teachers, the remainder are pupils. Find the fraction of pupils present. If there are 64 pupils present, how many people are in the meeting? How many parents present?

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